Integral Calculator

Discover the simplicity and efficiency of computing antiderivatives with our online tool. Simply enter your functions below to obtain their antiderivatives along with step-by-step calculations.

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Online Integral Calculator

This tool allows for online calculation of a function's integral. It accepts common functions such as polynomial, exponential, logarithmic, trigonometric functions, and more.

Importance of Integrals in Mathematics

The integral, or indefinite integral, of a function is key in mathematics, especially in analysis and physics. Finding an integral means determining a function whose derivative is the given function, which is essential for understanding concepts like the area under a curve or solving differential equations.

How to Use the Calculator

To use this integral calculator, follow these simple steps:

Enter the main variable (for example x).
Input the function of which you wish to find the integral (for example x^2).

Data Entry Guide

This guide will help you correctly enter data into the calculator:

Variables	A function can have one or more variables, but only one main variable. A variable is a single lowercase or uppercase letter. Examples: A function f with one main variable : f(x) = 4x A function g with one main variable x and a secondary parameter m, g(x) = 4x*m + x + 1, In this case, enter x in the “main variable” field
Numbers	Use a dot as decimal separator
Operators	+ (addition), - (substration), * (multiplication), / (division), ^ (power), For multiply operator, enter ab not a.b nor ab. Example: 2x.
Constants	You may use these constants : pi (approx. 3.14), e (approx. 2,72) Examples: f(x) = pi * x or f(x) = e * (x+1+2*e)²
Common Functions	You may use theses functions in the expression of f(x) sqrt(x) (square root), exp(x) (exponential function), log(x) or ln (natural logarithm),
Trigonometric functions	You may use theses functions in the expression of f(x) sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), csc (cosecant),
Inverse trigonometric functions	You may use theses functions in the expression of f(x) arcsin (arcsine), arccos (arccosine), arctan (arctangent), arccot (arcotangent), arcsec (arcsecant), arccsc (arccosecant),
Hyperbolic Functions	You may use theses functions in the expression of f(x) sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), coth (hyperbolic cotangent), sech (hyperbolic secante), csch (hyperbolic cosecant)
Inverse hyperbolic functions	You may use theses functions in the expression of f(x) asinh (inverse hyperbolic sine), acosh (inverse hyperbolic cosine), atanh (inverse hyperbolic tangent), acoth (inverse hyperbolic cotangent), asech (inverse hyperbolic secant), acsch (inverse hyperbolic cosecant)

Table of basic functions primitives

Fonction f(x)	Primitive
`k` where `k in RR`	`k*x+C`
`x^n` where `n in NN`*	`x^(n+1)/(n+1)+C`
`1/x`	`ln(\|x\|)+C`
`1/x^n` where `n in NN , n >=2`	`-1/((n-1)x^(n-1))+C`
`sqrt(x)`	`frac{2}{3}xsqrt(x)+C`
`1/sqrt(x)`	`-1/(2xsqrt(x))+C`
`sin(x)`	`-cos(x)+C`
`cos(x)`	`sin(x)+C`
`ln(x)`	`x*ln(x)-x+C`
`e^x`	`e^x+C`

Table of composite functions primitives

Fonction composée	Primitive
`u'*u`	`u^2/2+C`
`(u')/u^2`	`-1/u+C`
`u'*u^n` where `n in NN\text{ and }n != -1`	`u^(n+1)/(n+1)+C`
`(u')/u^n` where `n in NN\text{ and }n >= 2`	`1/((n-1)*u^(n-1))+C`
`(u')/sqrt(u)`	`2*sqrt(u)+C`
`(u')/u`	`ln(\|u\|)+C`
`u'*e^u`	`e^u+C`
`u'*sin(u)`	`-cos(u)+C`
`u'*cos(u)`	`sin(u)+C`
`u'*u^a` where `a in RR\text{ and }a != -1`	`u^(a+1)/(a+1)+C`
`u'*g(u)`	`g(u)+C`

Conclusion

Our online integral calculator is an intuitive and powerful tool, ideal for students, teachers, and professionals. It simplifies finding integrals, making learning and applying mathematics easier. We invite you to use it to explore mathematical concepts and enhance your understanding of functions and their integration.